Name: Sampling Distributions for Means
Uploaded: 2020-02-18T01:00:00.000Z
Description: We build sampling distributions for x-bar using a simulator, then review the formulas and facts associated with sampling distribution. We finish with a practice MC and FRQ problem.

AP Statistics

Unit 1 – Exploring One–Variable Data

Unit 2 – Exploring Two–Variable Data

Unit 3 – Collecting Data

Unit 4 – Probability, Random Variables, and Probability Distributions

Unit 5 – Sampling Distributions

Unit 6 – Proportions

Unit 7 – Means

Unit 8 – Chi–Squares

Unit 9 – Slopes

Frequently Asked Questions

Previous Exam Prep

AP Cram Sessions 2021

Live Cram Sessions 2020

January

Past Events

Study Tools

Exam Skills

We build sampling distributions for x-bar using a simulator, then review the formulas and facts associated with sampling distribution. We finish with a practice MC and FRQ problem.

What is Statistics?

What's the Point of Statistics?

Context of Data

Describing Data

Unit 1 Overview: Exploring One-Variable Data

Statistics & Data, Data, Data

Going Deeper into Data and the "W"s

Introducing Statistics: What Can We Learn from Data?

Intro to Z-Scores

Normal Model: More than Just a Hump

The Empirical (68–95–99.7) Rule

Practice Problems

The Normal Distribution

Types of Variables

Going Deeper: Categorical vs. Quantitative Variables

Example Question

The Language of Variation: Variables

Frequency Tables

Extension: Relative Frequency Tables

Representing a Categorical Variable with Tables

Bar Graphs

Pie Charts

Contingency Table (Two-Way Table)

Real-Life Applications: To Trust or Not To Trust a Bar/Pie Chart?

Representing a Categorical Variable with Graphs

Representing a Quantitative Variable with Graphs

Describing the Distribution of a Quantitative Variable

Statistics of Center

Statistics of Spread

A Note About Outliers

Summary Statistics for a Quantitative Variable

Five Number Summaries

Box Plots

Practice Questions

Graphical Representations of Summary Statistics

Comparing Groups with Stem-and-Leaf Plots: Warm Up

Comparing Groups with Histograms: Practice AP-Style Problem

Comparing Groups with Box Plots: Practice AP-Style Problem

Comparing Distributions of a Quantitative Variable

Unit 1 – Exploring One-Variable Data

Exam Weighting

Bivariate Data 🧠

Computer Outputs 🖥️

Mathematical Practices 🧮

Main Ideas for this Unit

Unit 2 Overview: Exploring Two-Variable Data

Types of Data 

How Can I Use This Data?

Introducing Statistics: Are Variables Related?

Various Tables and Diagrams

Determining Associations from Graphical Representations

Representing Two Categorical Variables

Additional Relative Frequencies

Determining Associations from a Two-Way Table

Vocabulary Practice from 2.1 to 2.3 Material

Statistics for Two Categorical Variables

What is a Scatterplot? ❓

Describing Scatterplots 🗒️

Example

Representing the Relationship Between Two Quantitative Variables

Calculating the Correlation Coefficient

Correlation

What is a LSRL?

Extrapolation

Practice Problem

Linear Regression Models

Residual Plots

Good or Bad? 🧐

Calculating Residuals

Residuals

LSRL—Slope

LSRL—y-intercept

LSRL—Coefficient of Determination

LSRL—Standard Deviation of the Residuals

Reading a Computer Printout

Least Squares Regression

Influential Points

Transforming Data and Nonlinear Regression

Analyzing Departures from Linearity

Unit 2 – Exploring Two-Variable Data

How Do We Approach Data Collection?

Unit 3 Overview: Collecting Data

📊 Data: Truth-Revealing or Deceiving?

Introducing Statistics: Do the Data We Collected Tell the Truth?

Introduction to Planning a Study

Types of Non-Biased Sampling Methods 

Random Sampling and Data Collection

Bias in Sampling 

Why does this matter, then? 

Potential Problems with Sampling

🗃 Components of an Experiment

🖋 Elements of a Well-Designed Experiment

🗄 Types of Experiments

Introduction to Experimental Design

Essential Knowledge

Selecting an Experimental Design

Inferences for Studies/Samples

Inferences for Experiments

Inference and Experiments

Probability: What are the Odds?

Probability Rules

Probability Distributions

Unit 4 Overview:  Probability, Random Variables, and Probability Distributions

🌐 Daily Experiences 

📊 Statistical Significance

🤔 Examples, Examples, Examples: Random vs. Non-Random Patterns

Introducing Statistics: Random and Non-Random Patterns?

Binomial Basics

Introduction to the Binomial Distribution

Parameters for a Binomial Distribution

Binomial vs. Geometric: Spot the Difference!

Calculating Probabilities

Shape, Center, and Variability

The Geometric Distribution

Simulation Time!

Estimating Probabilities Using Simulation

📝 Basic Probability Rules 

Probabilities and Context

Introduction to Probability

Intersections and Mutually Exclusive Events

Practice Problem #1

Practice Problem #2

Mutually Exclusive Events

Representations of Probability 

Conditional Probability

Independent Events and Unions of Events

❓ Types of Random Variables

🫂 Probability Distributions = Best Friend!

🧠 Example

Introduction to Random Variables and Probability Distributions

Mean and Standard Deviation of Random Variables

Linear Transformations of a Random Variable

Combining Random Variables

Unit 4 – Probability, Random Variables, & Probability Distributions

What is a Sampling Distribution?

Sampling Distribution for Proportions

Sampling Distribution for Means

Sampling Distributions for the Differences in Means and Proportions

Unit 5 Overview: Sampling Distributions

Sampling Distributions... Defined

Parameters vs. Statistics

Introducing Statistics: Why Is My Sample Not Like Yours?

Empirical Rule Review

The Normal Distribution, Revisited

Definition

The Central Limit Theorem

How to Tell if a Sample is Unbiased

Bias and Variability

Biased and Unbiased Point Estimates

Formulas

Large Counts Condition

Sampling Distributions for Sample Proportions

Differences (Non-Distribution) Recap

Proportion Differences

Sampling Distributions for Differences in Sample Proportions

Normal Condition: Central Limit Theorem

Sampling Distributions for Sample Means 

Sampling Distributions for Differences in Sample Means

Inference Who?

Confidence Intervals

Significance Tests

Inference with Two Proportions

Unit 6 Overview: Inference for Categorical Data: Proportions

What does it mean to be normal?

Why is it important?

How do we know if it is normal?

Introducing Statistics: Why Be Normal?

Hypotheses and Parameters

Conditions

Setting Up a Test for the Difference of Two Population Proportions

Calculating Values

Concluding the Test

Continued Example

Carrying Out a Test for the Difference of Two Population Proportions

Checking Conditions

One Sample z-interval for Proportions

Calculating the Interval

Constructing a Confidence Interval for a Population Proportion

Concluding a Confidence Interval

The Big Three

Testing a Claim Using Intervals

Sample Size, Confidence Interval Width, Confidence Level, and Margin of Error

Justifying a Claim Based on a Confidence Interval for a Population Proportion

Sampling Distributions for Means

Sampling Distributions for Means

AP Statistics 📊

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